Are our colleges equipping women to be leaders?

As we near the March release of Sheryl Sandberg’s book about women and the workplace, I’ve been thinking back to the Facebook chief operating officer’s 2011 commencement address at Barnard College. It was the speech that really debuted her language and thinking on the need for women to “lean in” to their careers. Two years later, that phrase is the title of her much anticipated hardback.

“[If] all young women start to lean in, we can close the ambition gap right here, right now, if every single one of you leans in,” Sandberg said back then to Barnard’s graduating class.

In the time since, her words have mostly been applied in the context of the business world, as a call to fight for seats in the boardrooms and upper-management meetings where women are still largely absent. Yet the words first resounded on a campus, and it’s interesting to look at what “leaning in” means in the context of this country’s colleges and universities.

Women now make up the majority of higher-education students, both at the undergraduate and graduate level. They also lead 26 percent of universities in the United States. That’s a small number, but it is significantly higher than the 4 percent of female CEOs who run Fortune 500 companies. Perhaps even more striking, five of the eight schools that comprise the Ivy League — institutions with strong traditions and images as old boys’ clubs — have female presidents at their helm.

Yet despite higher education’s growing ranks of female students and leaders, there are persistent problems for both sets. On the leadership side, women still hold the minority of faculty positions. Even at the University of Pennsylvania, for example, which has a female president and which has prioritized increasing its faculty diversity, women make up 25 percent of academic leaders (such as deans and department chairs) and an even smaller percentage of the overall faculty. And this is one of the more committed schools.

Perhaps some of these numbers reflect what Sandberg calls “the ambition gap,” or women’s propensity to shy away at points in their careers — management opportunities, for example — where men typically lean in.

But is “leaning in” really also the problem for young women in their early twenties, who are just leaving prestigious schools like Barnard to start their careers?

It wouldn’t seem so, and yet the pay gap kicks in the moment women hit the workforce. Just a year out of college, female graduates make 82 cents for every dollar that male graduates make.

It raises the question of what college campuses are doing, both for their own leadership set and for the students they are educating, to create and support more female professionals.

From time to time, we pull together a virtual round table for the Washington Post’s On Leadership section, where we invite several experts to write op-eds on the same subject but from different perspectives. This time, we asked three female presidents — Amy Gutmann of the University of Pennsylvania, Georgia Nugent of Kenyon College and Debora Spar of Barnard College — to share their thoughts on the these issues facing women in higher education today.

Where Gutmann focused more broadly on the pipeline for women at the leadership level of universities, Nugent took the opportunity to share her own personal experience navigating the ascent of academia. And Spar had an altogether different approach. She traced how the pay gap for new graduates reflects two systemic educational problems: that “the university experience is still an unequal one,” and that schools still don’t “focus on the economic consequences of our students’ years on campus.”

Spar, in fact, was the one who invited Sandberg to deliver the Barnard commencement address. It’s worth reading all three women’s accounts of what “leaning in” does and doesn’t, should and shouldn’t, look like in higher education today. And it’s worth thinking about where encouraging such “leaning in” for young women ends, and where encouraging it in our educational institutions begins.